FPT (complexity class)¶

A parameterized problem that allows for such an FPT algorithm is said to be a fixed-parameter tractable problem and belongs to the class , and the early name of the theory of parameterized complexity was fixed-parameter tractability.

Version: v1 · 2026-09-28 · History
Domain-specific #: 9554
Domain group: Applied Sciences & Engineering
Origin domain: Computer Science & Software Engineering
Subdomains: Parameterized Complexity, Computational Complexity → Computer Science & Software Engineering

Core Idea¶

FPT (complexity class) is treated here as the recurring computing and information systems identity summarized by this source-grounded definition: A parameterized problem that allows for such an FPT algorithm is said to be a fixed-parameter tractable problem and belongs to the class , and the early name of the theory of parameterized complexity was fixed-parameter tractability. In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output.

Scope of Application¶

Documented setting. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number.
Setup. In many applications, for example when modelling error correction, one can assume the parameter to be "small" compared to the total input size.
Setup. A parameterized problem is fixed-parameter tractable if the question " (x, k) \in L ?" can be decided in running time f(k) \cdot |x|^{O(1)} , where is an arbitrary function depending.
Complexity classesFPT. FPT (fixed parameter tractable) is the class of decision problems decidable in deterministic time f(k) \cdot ^{O(1)} , where is a computable function.
Complexity classesFPT. Typically, this function is thought of as single exponential, such as 2^{O(k)} , but the definition admits functions that grow even faster.

Clarity¶

A clear use of FPT (complexity class) names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is A parameterized problem that allows for such an FPT algorithm is said to be a fixed-parameter tractable problem and belongs to the class , and the early name of the theory of parameterized complexity was fixed-parameter tractability.

Manages Complexity¶

FPT (complexity class) compresses multiple computing and information systems details into a stable diagnostic relation. The source shows both the central mechanism—a computational trace through the Turing machine is then fully specified by setting k variables of s{t, i, j, a, b} to True to indicate the Turing machine state transitions at each time, and setting k^2 variables of y{t, p, a, b} to True to.

Abstract Reasoning¶

Type the carrier. Identify the computing and information systems entities to which the claim applies.
State the relation. Use the source-grounded identity: A parameterized problem that allows for such an FPT algorithm is said to be a fixed-parameter tractable problem and belongs to the class , and the early name of the theory of parameterized complexity was fixed-parameter tractability.
Check operation and conditions. Many problems have the following form: given an object and a nonnegative integer , does have some property that depends on ? 4.

Knowledge Transfer¶

Within the home domain. Knowledge about FPT (complexity class) transfers literally when a new case preserves the same carrier type, relation, and recognition test. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured as a function of the number of bits in the input. In many applications, for example when modelling error correction, one can assume the parameter.

Relationships to Other Abstractions¶

Current abstraction FPT (complexity class) Domain-specific

Parents (1) — more general patterns this builds on

FPT (complexity class) is a kind of Complexity Class Domain-specific

FPT is a complexity class defined by fixed-parameter tractable running-time bounds.

Neighborhood in Abstraction Space¶

FPT (complexity class) sits in a moderately populated region (59^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Computation Models & Complexity Classes (37 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08